pacman::p_load(olsrr, corrplot, ggpubr, sf, spdep, GWmodel, tmap, tidyverse, gtsummary)Hands-on Exercise 10: Calibrating Hedonic Pricing Model for Private Highrise Property with Geographically weighted regression (GWR)
In this exercise, I am applying GWR to develop hedonic pricing models, where structural and locational variables are used to model 2015 resale condo prices.
R Packages used
OLS and performing diagnostics tests
Calibrating geographical weighted family of models
Multivariate data visualisation and analysis
Spatial data handling
- sf
Attribute data handling
- tidyverse, especially readr, ggplot2 and dplyr
Choropleth mapping
- tmap
GW models suit situations when data are not described well by some global model, but where there are spatial regions where a suitably localised calibration provides a better description.
GWmodel includes functions to calibrate: GW summary statistics, GW principal components analysis, GW discriminant analysis and various forms of GW regression; some of which are provided in basic and robust (outlier resistant) forms.
Discriminant analysis
used to analyze data when the dependent variable is categorical and the independent variable is interval in nature
Data
URA Master Plan subzone boundary
mpsz <- st_read(dsn = 'data/geospatial/', layer = 'MP14_SUBZONE_WEB_PL')Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/williamtjw/is415-gaa-williamtjw/resources/Hands-on_Ex/ex10/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21
Resale prices of condominium in 2015
condo_resale <- read_csv('data/aspatial/Condo_resale_2015.csv')Rows: 1436 Columns: 23
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
dbl (23): LATITUDE, LONGITUDE, POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_...
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
Wrangling
URA Master Plan subzone boundary
Since mpsz does not have EPSG information, use st_tranform() to modify the projection of mpsz
mpsz_3414 <- st_transform(mpsz, 3414)
# to verify
st_crs(mpsz)Coordinate Reference System:
User input: SVY21
wkt:
PROJCRS["SVY21",
BASEGEOGCRS["SVY21[WGS84]",
DATUM["World Geodetic System 1984",
ELLIPSOID["WGS 84",6378137,298.257223563,
LENGTHUNIT["metre",1]],
ID["EPSG",6326]],
PRIMEM["Greenwich",0,
ANGLEUNIT["Degree",0.0174532925199433]]],
CONVERSION["unnamed",
METHOD["Transverse Mercator",
ID["EPSG",9807]],
PARAMETER["Latitude of natural origin",1.36666666666667,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8801]],
PARAMETER["Longitude of natural origin",103.833333333333,
ANGLEUNIT["Degree",0.0174532925199433],
ID["EPSG",8802]],
PARAMETER["Scale factor at natural origin",1,
SCALEUNIT["unity",1],
ID["EPSG",8805]],
PARAMETER["False easting",28001.642,
LENGTHUNIT["metre",1],
ID["EPSG",8806]],
PARAMETER["False northing",38744.572,
LENGTHUNIT["metre",1],
ID["EPSG",8807]]],
CS[Cartesian,2],
AXIS["(E)",east,
ORDER[1],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]],
AXIS["(N)",north,
ORDER[2],
LENGTHUNIT["metre",1,
ID["EPSG",9001]]]]
Reveal the extent of mpsz_3414
# Returns bounding of a simple feature or simple feature set
st_bbox(mpsz_3414) xmin ymin xmax ymax
2667.538 15748.721 56396.440 50256.334
Resale prices of condominium in 2015
summary(condo_resale) LATITUDE LONGITUDE POSTCODE SELLING_PRICE
Min. :1.240 Min. :103.7 Min. : 18965 Min. : 540000
1st Qu.:1.309 1st Qu.:103.8 1st Qu.:259849 1st Qu.: 1100000
Median :1.328 Median :103.8 Median :469298 Median : 1383222
Mean :1.334 Mean :103.8 Mean :440439 Mean : 1751211
3rd Qu.:1.357 3rd Qu.:103.9 3rd Qu.:589486 3rd Qu.: 1950000
Max. :1.454 Max. :104.0 Max. :828833 Max. :18000000
AREA_SQM AGE PROX_CBD PROX_CHILDCARE
Min. : 34.0 Min. : 0.00 Min. : 0.3869 Min. :0.004927
1st Qu.:103.0 1st Qu.: 5.00 1st Qu.: 5.5574 1st Qu.:0.174481
Median :121.0 Median :11.00 Median : 9.3567 Median :0.258135
Mean :136.5 Mean :12.14 Mean : 9.3254 Mean :0.326313
3rd Qu.:156.0 3rd Qu.:18.00 3rd Qu.:12.6661 3rd Qu.:0.368293
Max. :619.0 Max. :37.00 Max. :19.1804 Max. :3.465726
PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_HAWKER_MARKET PROX_KINDERGARTEN
Min. :0.05451 Min. :0.2145 Min. :0.05182 Min. :0.004927
1st Qu.:0.61254 1st Qu.:3.1643 1st Qu.:0.55245 1st Qu.:0.276345
Median :0.94179 Median :4.6186 Median :0.90842 Median :0.413385
Mean :1.05351 Mean :4.5981 Mean :1.27987 Mean :0.458903
3rd Qu.:1.35122 3rd Qu.:5.7550 3rd Qu.:1.68578 3rd Qu.:0.578474
Max. :3.94916 Max. :9.1554 Max. :5.37435 Max. :2.229045
PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_TOP_PRIMARY_SCH
Min. :0.05278 Min. :0.02906 Min. :0.07711 Min. :0.07711
1st Qu.:0.34646 1st Qu.:0.26211 1st Qu.:0.44024 1st Qu.:1.34451
Median :0.57430 Median :0.39926 Median :0.63505 Median :1.88213
Mean :0.67316 Mean :0.49802 Mean :0.75471 Mean :2.27347
3rd Qu.:0.84844 3rd Qu.:0.65592 3rd Qu.:0.95104 3rd Qu.:2.90954
Max. :3.48037 Max. :2.16105 Max. :3.92899 Max. :6.74819
PROX_SHOPPING_MALL PROX_SUPERMARKET PROX_BUS_STOP NO_Of_UNITS
Min. :0.0000 Min. :0.0000 Min. :0.001595 Min. : 18.0
1st Qu.:0.5258 1st Qu.:0.3695 1st Qu.:0.098356 1st Qu.: 188.8
Median :0.9357 Median :0.5687 Median :0.151710 Median : 360.0
Mean :1.0455 Mean :0.6141 Mean :0.193974 Mean : 409.2
3rd Qu.:1.3994 3rd Qu.:0.7862 3rd Qu.:0.220466 3rd Qu.: 590.0
Max. :3.4774 Max. :2.2441 Max. :2.476639 Max. :1703.0
FAMILY_FRIENDLY FREEHOLD LEASEHOLD_99YR
Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.4868 Mean :0.4227 Mean :0.4882
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000
condo_resale_sf <- condo_resale %>% st_as_sf(coords = c('LONGITUDE','LATITUDE'), crs=4326) %>%
st_transform(crs=3414) condo_resale_sfSimple feature collection with 1436 features and 21 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 14940.85 ymin: 24765.67 xmax: 43352.45 ymax: 48382.81
Projected CRS: SVY21 / Singapore TM
# A tibble: 1,436 × 22
POSTCODE SELLING_PRICE AREA_SQM AGE PROX_CBD PROX_CHILDCARE
* <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 118635 3000000 309 30 7.94 0.166
2 288420 3880000 290 32 6.61 0.280
3 267833 3325000 248 33 6.90 0.429
4 258380 4250000 127 7 4.04 0.395
5 467169 1400000 145 28 11.8 0.119
6 466472 1320000 139 22 10.3 0.125
7 309502 3410000 218 24 4.24 0.326
8 468497 1420000 141 24 11.6 0.162
9 118450 2025000 165 27 6.46 0.123
10 268157 2550000 168 31 6.52 0.609
# ℹ 1,426 more rows
# ℹ 16 more variables: PROX_ELDERLYCARE <dbl>, PROX_URA_GROWTH_AREA <dbl>,
# PROX_HAWKER_MARKET <dbl>, PROX_KINDERGARTEN <dbl>, PROX_MRT <dbl>,
# PROX_PARK <dbl>, PROX_PRIMARY_SCH <dbl>, PROX_TOP_PRIMARY_SCH <dbl>,
# PROX_SHOPPING_MALL <dbl>, PROX_SUPERMARKET <dbl>, PROX_BUS_STOP <dbl>,
# NO_Of_UNITS <dbl>, FAMILY_FRIENDLY <dbl>, FREEHOLD <dbl>,
# LEASEHOLD_99YR <dbl>, geometry <POINT [m]>
EDA using ggplot2
Univariate
SELLING_PRICE
Code
ggplot(data=condo_resale_sf, aes(x=`SELLING_PRICE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
Since it has a right-skewed distribution, normalise using logarithmic transformation.
LOG_SELLING_PRICE
condo_resale_sf <- condo_resale_sf %>%
mutate(`LOG_SELLING_PRICE` = log(SELLING_PRICE))SELLING_PRICE vs LOG_SELLING_PRICE
Code
ggplot(data=condo_resale_sf, aes(x=`SELLING_PRICE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
ggplot(data=condo_resale_sf, aes(x=`LOG_SELLING_PRICE`)) +
geom_histogram(bins=20, color="black", fill="light blue")

Multivariate (Trellis)
Code
AREA_SQM <- ggplot(data=condo_resale_sf, aes(x= `AREA_SQM`)) +
geom_histogram(bins=20, color="black", fill="light blue")
AGE <- ggplot(data=condo_resale_sf, aes(x= `AGE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_CBD <- ggplot(data=condo_resale_sf, aes(x= `PROX_CBD`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_CHILDCARE <- ggplot(data=condo_resale_sf, aes(x= `PROX_CHILDCARE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_ELDERLYCARE <- ggplot(data=condo_resale_sf, aes(x= `PROX_ELDERLYCARE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_URA_GROWTH_AREA <- ggplot(data=condo_resale_sf,
aes(x= `PROX_URA_GROWTH_AREA`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_HAWKER_MARKET <- ggplot(data=condo_resale_sf, aes(x= `PROX_HAWKER_MARKET`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_KINDERGARTEN <- ggplot(data=condo_resale_sf, aes(x= `PROX_KINDERGARTEN`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_MRT <- ggplot(data=condo_resale_sf, aes(x= `PROX_MRT`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_PARK <- ggplot(data=condo_resale_sf, aes(x= `PROX_PARK`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_PRIMARY_SCH <- ggplot(data=condo_resale_sf, aes(x= `PROX_PRIMARY_SCH`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_TOP_PRIMARY_SCH <- ggplot(data=condo_resale_sf,
aes(x= `PROX_TOP_PRIMARY_SCH`)) +
geom_histogram(bins=20, color="black", fill="light blue")
ggarrange(AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE,
PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT,
PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH,
ncol = 3, nrow = 4)
Statistical Point Map
tmap_mode("view")tmap mode set to interactive viewing
Code
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz_3414)+
tm_polygons() +
tm_shape(condo_resale_sf) +
tm_dots(col = "SELLING_PRICE",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))Warning: The shape mpsz_3414 is invalid (after reprojection). See
sf::st_is_valid
tmap_mode("plot")tmap mode set to plotting
Hedonic Pricing Models in R using lm()
Simple Linear Regression
Obtain and print a summary analysis
Code
condo_slr <- lm(
SELLING_PRICE ~ AREA_SQM,
condo_resale_sf)
summary(condo_slr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM, data = condo_resale_sf)
Residuals:
Min 1Q Median 3Q Max
-3695815 -391764 -87517 258900 13503875
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -258121.1 63517.2 -4.064 5.09e-05 ***
AREA_SQM 14719.0 428.1 34.381 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 942700 on 1434 degrees of freedom
Multiple R-squared: 0.4518, Adjusted R-squared: 0.4515
F-statistic: 1182 on 1 and 1434 DF, p-value: < 2.2e-16
SESELLING_PRICE = 14719*AREA_SQM - 258121.1
R-squared = 0.4518 (model is able to explain ~45% of actual condonresale prices
Model p-values <<< 0.001 (reject H0 that mean is a good estimator of SELLING_PRICE, hence there is sufficient statistic evidence that simple linear regression model above is a good estimator of SELLING_PRICE.
Both coefficient p-values <<< 0.001 (reject H0 … and can infer that both coefficients are good parameter estimates)
Visualise best fit curve on a scatterplot
Code
# using lm() as a method function
ggplot(data=condo_resale_sf,
aes(x=`AREA_SQM`, y=`SELLING_PRICE`)) +
geom_point() +
geom_smooth(method = lm)`geom_smooth()` using formula = 'y ~ x'

Multiple Linear Regression
Visualising the relationships of the independent variables (to identify highly correlated variables)
Code
# corrplot
corrplot(cor(
condo_resale[,5:23]),
diag = FALSE, # correlation coefficients are hidden
order = 'AOE',
tl.pos = 'td', # top-diagonal text labels
tl.cex = .5, # size of text labels
method = 'number', # visualisation method
type = 'upper' # displays upper half triangle of correlation matrix
)
Building the model
Code
# using lm()
condo_mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf)
summary(condo_mlr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET +
PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale_sf)
Residuals:
Min 1Q Median 3Q Max
-3475964 -293923 -23069 241043 12260381
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 481728.40 121441.01 3.967 7.65e-05 ***
AREA_SQM 12708.32 369.59 34.385 < 2e-16 ***
AGE -24440.82 2763.16 -8.845 < 2e-16 ***
PROX_CBD -78669.78 6768.97 -11.622 < 2e-16 ***
PROX_CHILDCARE -351617.91 109467.25 -3.212 0.00135 **
PROX_ELDERLYCARE 171029.42 42110.51 4.061 5.14e-05 ***
PROX_URA_GROWTH_AREA 38474.53 12523.57 3.072 0.00217 **
PROX_HAWKER_MARKET 23746.10 29299.76 0.810 0.41782
PROX_KINDERGARTEN 147468.99 82668.87 1.784 0.07466 .
PROX_MRT -314599.68 57947.44 -5.429 6.66e-08 ***
PROX_PARK 563280.50 66551.68 8.464 < 2e-16 ***
PROX_PRIMARY_SCH 180186.08 65237.95 2.762 0.00582 **
PROX_TOP_PRIMARY_SCH 2280.04 20410.43 0.112 0.91107
PROX_SHOPPING_MALL -206604.06 42840.60 -4.823 1.57e-06 ***
PROX_SUPERMARKET -44991.80 77082.64 -0.584 0.55953
PROX_BUS_STOP 683121.35 138353.28 4.938 8.85e-07 ***
NO_Of_UNITS -231.18 89.03 -2.597 0.00951 **
FAMILY_FRIENDLY 140340.77 47020.55 2.985 0.00289 **
FREEHOLD 359913.01 49220.22 7.312 4.38e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 755800 on 1417 degrees of freedom
Multiple R-squared: 0.6518, Adjusted R-squared: 0.6474
F-statistic: 147.4 on 18 and 1417 DF, p-value: < 2.2e-16
Revising the Model
[Remove] statistically insignificant variables
condo_mlr1 <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale_sf)[VIF] ols_vif_tol() - check multicolinearity
Code
ols_vif_tol(condo_mlr1) Variables Tolerance VIF
1 AREA_SQM 0.8728554 1.145665
2 AGE 0.7071275 1.414172
3 PROX_CBD 0.6356147 1.573280
4 PROX_CHILDCARE 0.3066019 3.261559
5 PROX_ELDERLYCARE 0.6598479 1.515501
6 PROX_URA_GROWTH_AREA 0.7510311 1.331503
7 PROX_MRT 0.5236090 1.909822
8 PROX_PARK 0.8279261 1.207837
9 PROX_PRIMARY_SCH 0.4524628 2.210126
10 PROX_SHOPPING_MALL 0.6738795 1.483945
11 PROX_BUS_STOP 0.3514118 2.845664
12 NO_Of_UNITS 0.6901036 1.449058
13 FAMILY_FRIENDLY 0.7244157 1.380423
14 FREEHOLD 0.6931163 1.442759
[Residual] ols_plot_resid_fit() - check linearity
Code
ols_plot_resid_fit(condo_mlr1)
[Residual] ols_plot_resid_hist() or
{#| output: true} #| code-fold: true{r} ols_plot_resid_hist(condo_mlr1)
[Stat. test] ols_test_normality() - check normality
Code
ols_test_normality(condo_mlr1)Warning in ks.test.default(y, "pnorm", mean(y), sd(y)): ties should not be
present for the one-sample Kolmogorov-Smirnov test
-----------------------------------------------
Test Statistic pvalue
-----------------------------------------------
Shapiro-Wilk 0.6856 0.0000
Kolmogorov-Smirnov 0.1366 0.0000
Cramer-von Mises 121.0768 0.0000
Anderson-Darling 67.9551 0.0000
-----------------------------------------------
Spatial autocorrelation test
Code
# save residual of the hedonic pricing model as a data frame
mlr_output <- as.data.frame(condo_mlr1$residuals)
# join with condo_resale_sf
condo_resale_res_sf <- cbind(condo_resale_sf, mlr_output) %>%
mutate(MLR_RES = condo_mlr1$residuals)
# convert condo_resale_res_sf into a SpatialPointsDataFrame
condo_resale_sp <- as_Spatial(condo_resale_res_sf)
condo_resale_spclass : SpatialPointsDataFrame
features : 1436
extent : 14940.85, 43352.45, 24765.67, 48382.81 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 24
names : POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE, PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT, PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH, PROX_SHOPPING_MALL, ...
min values : 18965, 540000, 34, 0, 0.386916393, 0.004927023, 0.054508623, 0.214539508, 0.051817113, 0.004927023, 0.052779424, 0.029064164, 0.077106132, 0.077106132, 0, ...
max values : 828833, 1.8e+07, 619, 37, 19.18042832, 3.46572633, 3.949157205, 9.15540001, 5.374348075, 2.229045366, 3.48037319, 2.16104919, 3.928989144, 6.748192062, 3.477433767, ...
tmap_mode("view")tmap mode set to interactive viewing
Code
tm_shape(mpsz_3414) +
tmap_options(check.and.fix = TRUE) +
tm_polygons(alpha = 0.4) +
tm_shape(condo_resale_res_sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))Warning: The shape mpsz_3414 is invalid (after reprojection). See
sf::st_is_valid
Variable(s) "MLR_RES" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
tmap_mode('plot')tmap mode set to plotting
Code
# Moran's I
# compute the distance-based weight matrix
nb <- dnearneigh(
coordinates(condo_resale_sp),
0, # lower bound
1500, # upper bound
longlat = FALSE
)
# convert nb into spatial weights
nb_lw <- nb2listw(nb, style = 'W')
# perform Moran's I
lm.morantest(condo_mlr1, nb_lw)
Global Moran I for regression residuals
data:
model: lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT +
PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale_sf)
weights: nb_lw
Moran I statistic standard deviate = 24.366, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
1.438876e-01 -5.487594e-03 3.758259e-05
Code
# summary(nb)
# summary(nb_lw)Generate publication-ready summary tables
Code
ols_regress(condo_mlr1) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751998.679
R-Squared 0.651 MSE 571471422208.592
Adj. R-Squared 0.647 Coef. Var 43.168
Pred R-Squared 0.638 AIC 42966.758
MAE 414819.628 SBC 43051.072
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000
Residual 8.120609e+14 1421 571471422208.592
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200
AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382
AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740
PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176
PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613
PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510
PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936
PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980
PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677
PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424
PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288
PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082
NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961
FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560
FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821
-----------------------------------------------------------------------------------------------------------------
OR,
Code
tbl_regression(condo_mlr1, intercept = TRUE) %>%
# include model statistics as a table source note
add_glance_source_note(
label = list(sigma ~ "\U03C3"),
include = c(
r.squared,
adj.r.squared,
AIC,
statistic,
p.value,
sigma))| Characteristic | Beta | 95% CI1 | p-value |
|---|---|---|---|
| (Intercept) | 527,633 | 315,417, 739,849 | <0.001 |
| AREA_SQM | 12,778 | 12,057, 13,498 | <0.001 |
| AGE | -24,688 | -30,092, -19,284 | <0.001 |
| PROX_CBD | -77,131 | -88,436, -65,826 | <0.001 |
| PROX_CHILDCARE | -318,473 | -530,250, -106,696 | 0.003 |
| PROX_ELDERLYCARE | 185,576 | 107,303, 263,849 | <0.001 |
| PROX_URA_GROWTH_AREA | 39,163 | 16,105, 62,222 | <0.001 |
| PROX_MRT | -294,745 | -406,394, -183,096 | <0.001 |
| PROX_PARK | 570,505 | 442,004, 699,006 | <0.001 |
| PROX_PRIMARY_SCH | 159,856 | 41,698, 278,014 | 0.008 |
| PROX_SHOPPING_MALL | -220,947 | -292,668, -149,226 | <0.001 |
| PROX_BUS_STOP | 682,482 | 418,616, 946,348 | <0.001 |
| NO_Of_UNITS | -245 | -418, -73 | 0.005 |
| FAMILY_FRIENDLY | 146,308 | 54,321, 238,295 | 0.002 |
| FREEHOLD | 350,600 | 255,448, 445,752 | <0.001 |
| R² = 0.651; Adjusted R² = 0.647; AIC = 42,967; Statistic = 189; p-value = <0.001; σ = 755,957 | |||
| 1 CI = Confidence Interval | |||
Code
# More info
# https://www.danieldsjoberg.com/gtsummary/articles/tbl_regression.htmlRDS
write_rds(mpsz_3414,'../ex11/data/rds/mpsz_3414.rds')
write_rds(condo_resale_sp,'../ex11/data/rds/condo_resale_sp.rds')